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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 72, 2017 - Issue 6
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Original Articles

Turbulent flow characteristics and heat transfer enhancement in a rectangular channel with elliptical cylinders and protrusions of various heights

, &
Pages 417-432 | Received 05 May 2017, Accepted 11 Sep 2017, Published online: 17 Oct 2017
 

ABSTRACT

This numerical study investigates turbulent flow characteristics and heat transfer augmentation in a rectangular channel with elliptical cylinders and protrusions. The height of protrusions is changed to quantify interactions with surrounding elliptical cylinders. Flow structures, temperature distributions, and heat transfer characteristics are obtained with a standard k − ε turbulence closure model. Cases are run at Reynolds numbers of 15,000 and 20,000. Combinations of protrusion and elliptical cylinder geometries give higher heat transfer rates than a case without protrusions. Additionally, Nusselt numbers increase with increases in height of protrusions and an optimum height-to-footprint diameter ratio is found.

Nomenclature

a, b=

the long and short radius of elliptical cylinders

D=

the footprint diameter of protrusions

Dh=

the hydraulic diameter of the channel

e=

the interval between the cylinder and protrusion

f=

the Fanning friction factor

f0=

the Fanning friction factor of the smooth channel

Gk=

the generation of turbulence kinetic energy due to the mean velocity gradients

Gb=

the generation of turbulence kinetic energy due to buoyancy

h=

the height of protrusions

k=

the turbulence kinetic energy

L=

the total length of the channel

L=

the feature length of the cylinder, i.e., the diameter of the cylinder

Nu=

the Nusselt number

Nu0=

the Nusselt number of the smooth channel

Nu(i)=

the local Nusselt number

p=

pressure

Pr=

the Prandtl numbers

qi=

the local heat flux

Re=

Reynolds number

S=

the distance between cylinders in the streamwise direction

Sk=

a user-defined source term

Sε=

a user-defined source term

T=

temperature

Tf=

the mean temperature

Ti=

the local temperature

uin=

the averaged inlet velocity to the channel

uz=

the dimensionless velocity along the z direction

YM=

the contribution of fluctuating dilatation in compressible turbulence

Δy=

the mesh size close the wall of bluff body

ΔP=

the inlet-to-outlet pressure drop

ε=

the rate of dissipation

λ=

the thermal conductivity of the fluid

μ=

the dynamic viscosity of the fluid

μt=

the turbulent viscosity

ρ=

flow density

σε=

the turbulent Prandtl number for ε

σk=

the turbulent Prandtl number for k

=

the local wall shear stress

Nomenclature

a, b=

the long and short radius of elliptical cylinders

D=

the footprint diameter of protrusions

Dh=

the hydraulic diameter of the channel

e=

the interval between the cylinder and protrusion

f=

the Fanning friction factor

f0=

the Fanning friction factor of the smooth channel

Gk=

the generation of turbulence kinetic energy due to the mean velocity gradients

Gb=

the generation of turbulence kinetic energy due to buoyancy

h=

the height of protrusions

k=

the turbulence kinetic energy

L=

the total length of the channel

L=

the feature length of the cylinder, i.e., the diameter of the cylinder

Nu=

the Nusselt number

Nu0=

the Nusselt number of the smooth channel

Nu(i)=

the local Nusselt number

p=

pressure

Pr=

the Prandtl numbers

qi=

the local heat flux

Re=

Reynolds number

S=

the distance between cylinders in the streamwise direction

Sk=

a user-defined source term

Sε=

a user-defined source term

T=

temperature

Tf=

the mean temperature

Ti=

the local temperature

uin=

the averaged inlet velocity to the channel

uz=

the dimensionless velocity along the z direction

YM=

the contribution of fluctuating dilatation in compressible turbulence

Δy=

the mesh size close the wall of bluff body

ΔP=

the inlet-to-outlet pressure drop

ε=

the rate of dissipation

λ=

the thermal conductivity of the fluid

μ=

the dynamic viscosity of the fluid

μt=

the turbulent viscosity

ρ=

flow density

σε=

the turbulent Prandtl number for ε

σk=

the turbulent Prandtl number for k

=

the local wall shear stress

Acknowledgments

A part of this work was performed using computing resources at the University of Minnesota Supercomputing Institute.

Additional information

Funding

The authors wish to thank the National Natural Science Foundation of China (51676163), the Fundamental Research Funds of Shaanxi Province (2015KJXX-12).

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